Finite Group Databasebeta

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Cayley diagram

C3×#4086 #91657

order480
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×#4086

Splittings

FittingC2×C3×C5×D4 ⋊ C2
HallC3×C5 ⋊ #127
SylowC5 ⋊ C3×#127

Subgroups

subgroupG/H
centerC22×C3C22×D5
commutator, cosocleC22×C5C23×C3
FrattiniC22C22×C3×D5
FittingC2×C3×C5×D4C2
socleC22×C3×C5C23
hypercenterC2×C3×D4D5
hypocenterC5C3×#127
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 16 points:

(1,2,4,5,3)(7,9)(11,13)(14,15,16);(10,13,12,11);(2,3)(4,5)(6,7)(8,9)(11,13)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746006, C3×#64694, C3×#64922, …
maximal normal subgroup of#11746006, C3×#64694, C3×#64922, …
maximal quotient ofC3×#65238, C3×#65246, C3×#65249, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 733);